When using the distributive property with negative numbers, I don't
understand when, why, and how the operator changes (from addition to
subtraction, or the other way). Sometimes it changes, sometimes it
doesn't. Can you explain when to change it, and why?

I'm trying to help my 7th grade class understand why subtracting an
integer is the same as adding its opposite, particularly in cases like
(-5) - (-3). Can you give real life examples or ideas on how to
explain this to them?

I'm finding it very difficult to imagine negative numbers outside of
math. In the real world, I can't have -$100 in my bank account. I
can't give away 6 apples when I only have 5 and be left with -1 apple.
How can the math be accurate but impossible?

Let's say 3 x 2 = 6. Three is how many kids there are in a 'group.'
Two is how many 'groups' there are, and six is the answer. Now let's
say 3 x (-2) = -6. How can you have negative two 'groups' of three
kids?